AUTHOR: BESS KUZMA, ST.PIUS X SCHOOL, AURORA, COLORADO

GRADE LEVEL: 5, 6, 7, 8

Subject(s):

• Mathematics/Number Theory

OVERVIEW:

Roman numerals are no longer an essential component of math, but need to be considered as a part of our cultural heritage.

PURPOSE:

Students are fascinated by the "secret code" aspect of Roman numerals. It can easily be integrated into a study of addition and subtraction, or world number systems.

OBJECTIVES:

1. Recognize Roman numerals as such when students see them.
2. Identify each symbol and what it stands for in Arabic numbers:

   I - 1
   V - 5
   X - 10
   L - 50
   C - 100
   D - 500
   M - 1000

3. Generally understand the source of each symbol. (See background information under RESOURCES)
4. Be able to transfer Roman numerals into Arabic numbers.
5. Be able to write the correct Roman numerals for Arabic numbers.
6. Have an appreciation for the historical value of Roman numerals, how they were used in the Roman Empire, and why they are no longer commonly used.

ACTIVITIES AND PROCEDURES:

1. Discuss the history of Roman numerals, using charts, photos, pictures, or whatever resources are available.
2. Have students make individual charts, showing each symbol and its equivalent in Arabic numbers.
3. Discuss the addition/subtraction aspects of the system, and have the students practice. Give each student 20-30 toothpicks, (the flat type), and form the Roman numerals for given Arabic numbers. For example, you might start with 106. Have the students make this, (CVI ), then have them change it to 206, (CCVI ), then 266, (CCLXVI ) then 466, (CDLXVI ), etc.
4. Have students write Roman numerals of family members' birth years, or the number of students in the school, or other large numbers of interest to them.
5. Let each student bring in an example or picture of Roman numerals (book preface paging or chapter numbers, watch or clock, building erection date, statue or monument, outline topic numbers, etc.)
6. Read books, articles, and encyclopedia entries about Roman numerals. Library skills could easily be incorporated.

RESOURCES/MATERIALS:

BACKGROUND:

Roman numerals were developed around 500 B.C. at least partially from primitive Greek alphabet symbols which were not incorporated into Latin. Using predominantly addition, they are read from left to right.

The symbol "I" for 1 was derived from one finger. Five fingers held up indicated five of whatever was being counted. The "V" then was the hand outstretched vertically with the space between the thumb and first finger forming the "V".

Originally the Greek letter "X", or "chi", meant 50, but in monument transcriptions it is easy to trace the original symbol's change to "L", and "X" came to mean 10. Another theory for "X" is that ten 1's were written in a row, and then crossed out with an "X" to simplify counting. Then the "X" alone became a shorthand version of 10. Yet another idea is that "V" looks like the top half of "X", as 5 is half of 10, and other scholars think that "V" doubled with an upside-down "V" meant 5 times 2, or "X". "C", indicating 100, came from the Latin word "centum", a hundred. (Also century, centennial, etc.) "M" is from "mille", a thousand. Larger numbers, like 5,000, are shown by putting a small bar called a "vinculum" above the "V" symbol, indicating multiplication by 1,000.

Until fairly recently a commonly used Roman numeral for 1,000 was "CI backwards C", derived from the Greek "phi", or "I" superimposed on "O". Half of this symbol, "I backwards C", led to "D" for 500, half of 1,000.

Generally, decoding Roman numerals is very straightforward. The largest numeral is at the left, with descending numerals moving to the right. Numbers are added as you go, as seen in these examples: CCLXVII - 200 + 50 + 10 + 5 + 1 + 1 = 267, MMMCCLXXXI - 1,000 + 1,000 + 1,000 + 100 + 100 + 50 + 10 + 10 + 10 + 1 = 3,281 and DCCXVII - 500 + 100 + 100 + 10 + 5 + 1 + 1 = 717.

Rather than continuing to add 1's to make 4 - "IIII" - or 9 - "VIIII" - subtraction was included in the computation of the numerals to simplify and shorten the resulting numbers. Therefore, 4 is shown "IV", or 5 minus 1. The smaller numeral BEFORE the larger one means subtract. "IX" is 9, or 10 minus 1. 40 is "XL", 50 minus 10; 90 is "XC", 100 minus 10; "CD" is 400, or 500 minus 100; and "CM" is 900, or 1,000 minus 100. Students can follow the principle that subtraction takes place ONLY when the smaller numeral is before the larger one, and involves 4 and 9 in various place values.

Obviously, the cumbersome aspect of Roman numerals is one of the main reasons that they have been replaced by the Arabic system in our daily mathematical lives. Roman numerals remain important as a part of the world's cultural past, and a unique way to express numbers.

REFERENCES:

Most encyclopedias have at least some information on Roman numerals, and several books on Roman numerals are appropriate for students. Three suggestions: "Number Art - Thirteen 1 2 3's from around the world", by Leonard Everett Fisher, published by Four Winds Press, NY, is a fairly sophisticated overview of world numerical systems. "Signs and Symbols Around the World", by Elizabeth Helfman, published by Lothrop, Lee & Shepard Co, NY, has a chapter on numerals of many cultures. There is a very short section on Roman numerals, but a great deal of general information about counting and mathematics applications throughout the world. "Roman Numerals", by David A. Adler, published by Thomas Y. Crowell Co, NY, is a much simpler book, but suitable for younger students.

TYING IT ALL TOGETHER:

Many alternatives are possible, depending upon allotted time for the unit, relative importance of the material in the curriculum, and the age of the students. Actual buildings or monuments could be visited, reports, games, or testing to ascertain student achievement are all possibilities.

May 1994

These lesson plans are the result of the work of the teachers who have attended the Columbia Education Center's Summer Workshop. CEC is a consortium of teacher from 14 western states dedicated to improving the quality of education in the rural, western, United States, and particularly the quality of math and science Education. CEC uses Big Sky Telegraph as the hub of their telecommunications network that allows the participating teachers to stay in contact with their trainers and peers that they have met at the Workshops.